1. Field of the Invention
The invention is directed to an arrangement for optical autocorrelation of laser speckle photography (LSP) photographs or particle image velocimetry (PIV) photographs using optical Fourier transforms.
2. Description of the Related Art
It is known to apply laser speckle photography (LSP) for accurate determination of the deformation state of surfaces. In so doing, the surface to be analyzed is irradiated by an expanded laser beam. The surface illuminated in this way is imaged on film material by means of a camera. As the result of a first exposure pulse, a corresponding speckle pattern is formed on the photographic material. If the surface moves or deforms after the initial exposure, the correspondingly changed laser speckle pattern is recorded on the same film material by a second laser exposure pulse. As a result of this double exposure, a pattern of speckle points is formed on the developed film material. In so doing, the spacing and orientation of two adjacent points indicates the magnitude of the surface change. In order to determine the displacement of the speckles along the film surface in a stepwise manner, the two-dimensional deformation profile or displacement vectors of the surface can be determined. An exact description of the method is given by Sirohi ("Speckle Merology", Marcel Dekker Inc., New York, Basel, Hong Kong (1993)) or Lauterborn ("Coherent Optics: Fundamentals for Physicists and Engineers", Berlin (1993)).
Similar point pictures are formed in the analysis of flow velocities and their two-dimensional distribution. The measuring method known as particle image velocimetry (PIV) is based on the fundamental principle of adding small particles to the flow so that these particles can follow the flow. When the flow to be analyzed is exposed by a laser light section, double exposure produces point pictures on the photographic material. The spacing and orientation of adjacent points characterize the velocity vector at the location in question. Given knowledge of the interval between the exposure pulses of the laser, the absolute velocity can be measured. When this spacing and orientation between the picture points is determined by scanning the film material, a corresponding network of two-dimensional velocity vectors is given. This method is extensively described by Adrian ("Particle-Image Techniques for Experimental Fluid Mechanics", Annu. Rev. Fluid Mech., 23, 261-304 (1991)) and also by Kurada et al. ("Particle-imaging techniques for quantitative flow visualization: a review", Optics & Laser Technology, 25, 219-232, (1993)).
For analysis of the above-mentioned photographic images, the point displacements must be determined in a stepwise manner as was described above. With a maximum size of the photographic image of 10.times.78 cm.sup.2, for example, there are 28,000 image fields to analyze on the photographic image given a spacing of approximately 0.5 mm between the operation units. Even with a small image film with a format of 24.times.36 mm.sup.2, there are still 3,456 operation units to be analyzed. Accordingly, the evaluation of the photographic materials is tedious. It has been the object of a number of studies to reduce the evaluation time.
The general approach used to determine the spacing between pairs of particle images is based on calculation of the autocorrelation function. A faster method is achieved by using Fourier transforms. As a result of the first Fourier transform of the particle image and subsequent squaring of the amount, Young's fringes are formed. A further Fourier transform of the Young's fringe pattern yields the autocorrelation function. This function is two-dimensional and ideally comprises three maxima in the amplitude distribution. The coordinates of the orders of diffraction mentioned above yield the direction and magnitude of the mean displacement of particles in the respective operation unit on the film image.
In EP-A-0422 212 (WO90/13036) Farrell describes an optical correlator for analyzing PIV photographs. The Young's fringe pattern is photographed by a CCD camera and written into an electrically addressable spatial light modulator (liquid crystal SLM). The second Fourier transform is then effected optically. The liquid crystal SLM serves as a reversible image storage. It is illuminated by a laser beam so that the autocorrelation function is recorded by a second CCD camera, followed by a search of the coordinates of the orders of diffraction. The disadvantage of this arrangement consists in the high cost of equipment. For example, two camera systems with corresponding electronic control units are required for recording the image and reproducing it on the matrix type spatial light modulator or on a computer for detecting the coordinates of the orders of diffraction. The use of liquid crystal matrix displays formed by commercially available TV's as electrically addressable spatial light modulators compels the use of large-aperture objectives due to the large dimensions of the liquid crystal SLMs (diagonal of several centimeters). Because of their large dimensions, these optical systems are prone to interference and cost-intensive. The use of a Faraday liquid crystal SLM with a pixel resolution of 48.times.48 described by Kompenhands et al. (Eighth International Congress on Applications of Lasers & Electro-Optics, Oct. 15-20, 1989, Orlando, U.S.A.) results in low accuracy in the evaluation of Young's fringes and accordingly has the disadvantages described above with reference to the digital Fourier transforms with low pixel numbers.
Coupland and Halliwell ("Automated Optical Analysis of Young's Fringes-Optical Autocorrelator", Opt. & Laser Eng., 14, 351-361 (1991) and "Particle imaging velocimetry: rapid transparency analysis using optical correlation, Appl. Opt., 27, 1919-1921, (1988)) describe an automatic optical correlator which uses an optically addressable SLM instead of an electrically addressable SLM. This liquid crystal SLM lies in the image-side focal plane of a first Fourier transform objective so that the Young's fringes are imaged on the SLM. An SLM produced from a BSO (bismuth silicon oxide) crystal changes its optical activity according to the projected exposure intensity. This change in optical activity can be reconstructed with a second laser. The optical autocorrelation is effected by means of a second Fourier transform arrangement so that only one CCD camera is required for peak detection in the autocorrelation plane. The long switching times of the BSO SLM in this arrangement are disadvantageous. For example, the relaxation times for the optical response of the SLM are approximately 0.5 to 1 s, which does not enable a substantial reduction in the evaluation time of the PIV photographs or LSP photographs. Further, activation of the BSO crystal on the write-in side requires a high-performance laser and a voltage supply of the BSO SLM of approximately 2 to 10 kV, which works out unfavorably for practical use.
Sharpe and Johnson ("Particle image velocimetry fringe processing using an optically addressed spatial light modulator", Appl. Opt., 31, 7399-7402 (1992)) describe the use of an optically addressed liquid crystal SLM with a ferroelectric liquid crystal layer (FLC). The utilized liquid crystal SLM is formed by a "photosemiconductor-FLC" sandwich system. The disadvantage of this liquid crystal SLM consists in the modulation of the readout light with two stable molecular positions typical of ferroelectric liquid crystals. This leads to a binarization of the Young's fringes. The second Fourier transform is effected with reduced data contents and consequently results in a less accurate autocorrelation function. The resulting disadvantage is a deterioration of the measuring accuracy of the optical autocorrelation arrangement.
This is also true of the arrangement with a FLC-liquid crystal SLM described by Mao, Halliwell and Coupland in "Particle imaging velocimetry. High-speed transparency scanning and correlation-peak location in optical processing systems" (Appl. Opt., 32, 5089-5091, (1993)).